decision problem – Randomized Polynomial time algorithm for bipartite perfect matching

I know that deciding whether there is a perfect matching in a given bipartite graph is in RP. Specifically, given a bipartite graph, one can show that there is polynomial-time randomised algorithm that answers “there is no perfect matching” w.p 1 when there is no perfect matching, and answers “there is a perfect matching” w.p at least 1/2 when there is a perfect matching.

My question is: how can I use the above algorithm to find a specific perfect matching (with the same one-sided error), and not only decide if there is a perfect matching?

I am familiar with the “Decision to Search in NP”, I tried to do something similar here, but did not succeed to bound the probability. Here is my attempt:

Given a Bipartite graph G = (V, E), use the above algorithm to decide if there is a perfect matching. If the answer is no, then answer “No”. If the answer is yes, consider some edge e = (u, v) in E, and remove u and v from the graph to get the graph G’. Then ask again if there is a perfect matching in G’. If the answer is yes, then a perfect matching M’ of G’ with the edge (u, v) are a perfect matching in G. Otherwise, if the answer is no, then we know that the edge (u, v) is not in any perfect matching of G. So, we remove the edge e from G (u and v remain in the graph), and we continue recursively.

Things that I know:

  1. If the algorithm that decides whether there is a perfect matching or not, is nonrandomised, then my suggestion actually produces a perfect matching of G, and it does so by applying the algorithm at most |E| times.

  2. I know that if a language has a randomised algorithm with one sided error 1/2, then the error can be amplified to $1/2^k$ where k is the length of the input.

I did not succeed to show that my suggestions works. That is, I did not succeed to show that it succeeds to produce a perfect matching w.p at least 1/2 when there is a perfect matching. (When there is no perfect matching, it clearly answers “No” w.p 1).

Thanks

Magento2 query displaying perfect result in database but wrong in collection while sorting by created_at

Magento2 query displaying perfect result in database but wrong in collection while sorting by created_at

Query

SELECT `e`.*, `cat_index`.`position` AS `cat_index_position`, `price_index`.`price`, `price_index`.`tax_class_id`, `price_index`.`final_price`, IF(price_index.tier_price IS NOT NULL, LEAST(price_index.min_price, price_index.tier_price), price_index.min_price) AS `minimal_price`, `price_index`.`min_price`, `price_index`.`max_price`, `price_index`.`tier_price`, IFNULL(review_summary.reviews_count, 0) AS `reviews_count`, IFNULL(review_summary.rating_summary, 0) AS `rating_summary` FROM `catalog_product_entity` AS `e` INNER JOIN `catalog_category_product_index_store1` AS `cat_index` ON cat_index.product_id=e.entity_id AND cat_index.store_id=1 AND cat_index.visibility IN(2, 4) AND cat_index.category_id=8 INNER JOIN `catalog_product_index_price` AS `price_index` ON price_index.entity_id = e.entity_id AND price_index.customer_group_id = 0 AND price_index.website_id = '1' LEFT JOIN `review_entity_summary` AS `review_summary` ON e.entity_id = review_summary.entity_pk_value AND review_summary.store_id = 1 AND review_summary.entity_type = (SELECT `review_entity`.`entity_id` FROM `review_entity` WHERE (entity_code = 'product')) ORDER BY `e`.`created_at` DESC

For sorting

$this->_collection
      ->getSelect()
        ->order('e.created_at');

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machine learning – Can the perceptron classifier achieve perfect accuracy, on any data set?

I was thinking. Since any data can become linearly seprabale through kernel methods, meaning there is a dimension where this data is linearly seprable, so feed this processed data set into the perceptron algorithm and then it might get to 100 percent accuracy.

Am I correct?

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Info on network and host nodes after the jump but first, here are the offers:

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KVM VPS

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Network information and node details available by reading more.

NETWORK INFO

Datacenter Name: DataPro – Russia, Moscow

Test IPv4: 45.67.230.12

Datacenter Name: Serverius – Netherlands, Meppel

Test IPv4: 193.38.54.15

Test IPv6: –

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Test IPv4: 45.67.229.16

Test IPv6: 2a09:7c46::990

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Test IPv4: 45.142.213.19

Test IPv6: –

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Test IPv4: 45.137.155.46

Test IPv6: –

Datacenter Name: Hong Kong

Test IPv4: 194.156.98.5

Test IPv6: –

Datacenter Name: vXchnge NJ-01 – USA, NJ, Secaucus

Test IPv4: 138.124.180.3

Test IPv6: –

Host Node Specifications:

Please let us know if you have any questions/comments and enjoy!

raindog308

I’m Andrew, techno polymath and long-time LowEndTalk community Moderator. My technical interests include all things Unix, perl, python, shell scripting, and relational database systems. I enjoy writing technical articles here on LowEndBox to help people get more out of their VPSes.